Anharmonic overtone generation in a computor organ

ABSTRACT

The production of musical notes containing anharmonic overtones is implemented in a computor organ of the type disclosed in U.S. patent application Ser. No. 225,883, filed Feb. 14, 1972, and now U.S. Pat. 3,809,786. In such an instrument, the sampled amplitudes of a musical waveshape are computed in real time by individually calculating the amplitude contributions of the Fourier components constituting the waveshape. In accordance with the present invention, certain of these Fourier components are evaluated at frequencies offset from multiples of the nominal fundamental frequency of the note being generated. This is accomplished by utilizing in the overtone amplitude calculations offset values Eta which establish the extent of anharmonicity of each overtone. This results in complete freedom of control of the anharmonicity of individual overtones. The overtone offset ( Eta ) values may be stored in a memory, or may be generated by appropriate circuitry. In certain embodiments the offset is proportional to the frequency of the note being produced, preferably being a constant number of cents. Other embodiments include, among other things, constant frequency offset independent of time, time variant anharmonicity, offset of alternate overtones in opposite frequency directions, and overtone selection to insure correct frequency of a subjective fundamental.

United States Patent Deutsch 1 1 ANHARMONIC OVERTONE GENERATION [N A COMPUTOR ORGAN [75] Inventor: Ralph Deutsch, Sherman Oaks,

Calif.

[73] Assignee: Nippon Gakki Seiko Kabushiki Kaisha, Hamamatsushi, Japan [22] Filed: June 28,1973

[21] Appl. No; 374,680

[52] U.S. C1. 1. 84/101; 84/103; 84/122; 235/152; 235/197 [51] Int. Cl.. ..G10h1/00;Gl0h 5/00 [58] Field of Search 84/101, 103, 1,24, 1.25. 84/D1G.4,D1G.5,l.11,119,122,123; 235/152, 197

[56] References Cited UNITED STATES PATENTS 3,000,252 9/1961 Wayne, Jr. 84/101 3,004,459 10/1961 Jones 84/101 3,004,460 10/1961 Wayne, Jr... 84/101 3,007,361 11/1961 WayneJrm, 84/10] 3,049,959 8/1962 Meyer 84/1124 3,147,333 9/1964 Wayne, Jr... 84/1124 3,157,725 11/1964 Wayne,Jr..,. 84/124 3,305,675 3/1967 Haase H 235/197 3,479,440 11/1969 Martin et a1. 84/125 3,633,017 l/1972 Crooke et a1. 235/152 X 3,636,337 1/1972 Dietcl et a1. .1 235/197 3,809,786 5/1974 Deutsch 84/101 3,809,788 5/1974 Deutschm, 84/101 3,809,789 5/1974 Deutsch 84/101 3,809,790 5/1974 Deutsch 8411.01 3,809,792 5/1974 Deutschm. 84/124 3,809,876 5/1974 Byram 235/197 3,831,015 8/1974 Hoff, Jr .1 235/197 OTHER PUBLICATIONS Richard A. Schaefer, Electronic Musical Tone Pro SINUSO'D TABLE [451 June 10, 1975 duction by Nonlinear Waveshaping, Journal of the Audio Engineering Society (USA), Aug. 1970, Vol. 18, No. 4, pp. 4l3417.

Primary Examiner-Richard B. Wilkinson Assistant Examiner-Stanley J Witkowski Attorney, Agent, or FirmAmbrose & Silber ABSTRACT The production of musical notes containing anharmonic overtones is implemented in a computor organ of the type disclosed in U.S. patent application Ser. No. 225,883, filed Feb. 14, 1972, and now US. Pat, 3,809,786. in such an instrument, the sampled amplitudes of a musical waveshape are computed in real time by individually calculating the amplitude contributions of the Fourier components constituting the waveshape. In accordance with the present invention, certain of these Fourier components are evaluated at frequencies offset from multiples of the nominal fundamental frequency of the note being generated. This is accomplished by utilizing in the overtone amplitude calculations offset values 1 which establish the extent of anharmonicity of each overtone. This results in complete freedom of control of the anharmonicity of individual overtones. The overtone offset (17,, values may be stored in a memory, or may be generated by appropriate circuitry. In certain embodiments the offset is proportional to the frequency of the note being produced, preferably being a constant number of cents. Other embodiments include, among other things, constant frequency offset independent of time, time variant anharmonicity, offset of alternate overtones in opposite frequency directions, and overtone selection to insure correct frequency of a subjective fundamental.

18 Claims, 13 Drawing Figures 5U VERTONE M v ADDR es OFFSETUL) HARMONC 1") 47 EMZZCDDER E MEMORY \MPLIYUDE 1 Accumum'rotz 4 MULTIPLIER LEA;

W I") 2/ 7 MEMolzv +6 clq 2; F

ADDK2E5$ n- 42 CONTQOL 2U nARMomc 28 58- p COEFFiClENT t nq 43 MEMORY 'l" A E 1 24 HARMONIC INTERVAL CLEAR L 26 --I none? 3/ 2 L L MEMOE" DlGl AL TO 37 GQYE l ADDRESS ANALOG F 36 /2 co NTER CONTROL CONVERTER N U q I? O NOTE INTEQVAL Q 2/ V RDDEI? GATE FREQUENCY (MODULO N) 27, NUMBER scum: eve-rem 34 MEMO?" -27 55 iNsrQUMENT KEYBOARD 22 swi'ro-is PATENTEDJUH 10 ms FROM MEYBOQTZD 5WITCH as 22 TO ADDER 21 (FIG 2) n-fm 45 iii pz ps COUNTER REGDSTER (srons 1 -55 27 FREQUENCV N BER MEMORY To GATE 34 (FIG. 2

DIVIDEQ 5Q 60 To REGiSTER 53 L FIG 3) CLEAR HZ-U, l 53 TO ADDEIZ 42 5% ADDEQ GATE (s'rorzs 8h) REGISTER 1G 'r- ADDER ,F IG 15' l rc. .8.

GATE

( sToQE T REGISTER OSCILLATOR A/D CONVERTER To ADDEQ ADDEQ .SUBJ ECT'IVE FUNDAMENTAL PATENTEDJUH I 0 I975 CLEAR ANHARMONIC ()VER'IONE GENERATION IN A COMPUTOR ORGAN BACKGROUND OF THE INVENTION 1. Related Applications The present invention is related to the following copending US. patent applications:

Ser. No. 225,883 COMPUTOR ORGAN, filed Feb.

I4, 1972. and now US. Pat. No, 3.809.786,

Ser. No. 298,365 COMPUTOR ORGAN USING PARALLEL PROCESSING. tiled Oct. l7, I972. and now US. Pat. No. 3,809,788.

Ser. No. 32l,23l PRODUCTION OF CELESTE IN A COMPUTOR ORGAN. filed Jan. 5. I973. and now US. Pat. No. 3,809,792.

Ser. No. 328.302 IMPLEMENTATION OF COM BINED FOOTAGE STOPS IN A COMPUTOR ORGAN, filed Jan. 3]. I973. and now US. Pat. No. 3.3U9,79(l.

The latter three applications are commonly owned by Nippon Gakki Seizo Kabushiki Kaisha, the owner of the present application.

2. Field of the Invention The present invention relates to the generation of musical sounds containing anharmonic overtones in a computor organ.

3. Description of the Prior Art The unique tonal quality of certain conventional musical instruments is attributable to the presence of overtones which are not true harmonics of the note being played. This anharmonicity of the overtones is particularly characteristic of struck string instruments such as the piano and harpsichord. In the past. electronic synthesis of musical sounds containing non-harmonic overtones has been seriously impeded by limitations inherent in known tone generation systems.

For example, in electronic organs of the type using separate oscillators for each note, overtones which are integral multiples of the oscillator fundamental frequency are readily obtainable. However, production of non-harmonic overtones requires a separate oscillator for each anharmonic or frequency offset overtone, adding considerably to instrument cost. In digital organs of the type wherein a complex waveshape is stored in memory and read out repetitively at a frequency established by the selected note, individual harmonics cannot be separately controlled Although the stored waveshape may be characteristic of a sound having non-harmonic overtones, the \vaveshape is fixed. It is W xo(qR) in) impossible to modulate dynamically the overtone anharmonicity. thereby preventing synthesis of certain musical sounds.

The computor organ described in the above mentioned US. Pat. application Ser. No. 225.883 is unique in that each Fourier component of the produced musical waveshape is generated individually. As a result, frequency offsetting of individual overtones is possible, and the principal object of the present invention is to provide overtone frequency offsetting in such a computor organ. The generation of musical sounds characterized by anharmonic overtones is implemented, facilitating realistic electronic synthesis of struck string instruments and of sounds characteristic of bells, chimes, violins. orchestral brass and reeds.

Another object is to provide a chorus or ensemble cf feet between stops of different footage generated simultaneously in a computor organ having combined footage (see the above mentioned US. patent application, Ser. No. 328,302). By using anharmonic overtones, the stops of different footage will be unlocked even when played with a single key. For example, in such a system the dominant tone ofa 4-foot voice is the second overtone of an 8-foot voice. By frequency offsetting this second overtone so that it is not a true harmonic of the 8 foot fundamental. the two voices are unlocked. A chorus or ensemble is produced. Such unlocking of voices is totally impossible in a digital organ of the type wherein a waveshape is repetitively read from storage.

A further object is to provide octave decoupling by using the inventive overtone frequency offset modulation. With such modulation, two tones played on the same stop will beat, even throug their nominal fundamental frequencies are exactly in octave relationship.

In accordance with usual musical terminology, the term *overtone" is used herein to refer to one of the higher tones which together with the fundamental comprises a complex musical tonev If the overtone has a frequency which is in integral multiple of the fundamental, it is a harmonic overtone, or simply, a harmonic." However, an overtone need not be integrally related in frequency to the fundamental, and if the overtone has a frequency which is not an integral multiple of the fundamental, it is a non-harmonic or anharmonic overtone. Thus as used herein in both the specification and claims, the term *anharmonic" means not harmonic or inharmonic.

SUMMARY OF THE INVENTION These and other objectives are achieved by providing anharmonic overtone generation systems for a computor organ of the type described in the above mentioned US. patent application Ser. No. 225,883. In such an instrument, musical notes are generated by computing the amplitudes at successive sample points of a musical waveshape and converting the amplitudes to musical sounds as the computations are carried out in real time. For each sample point qR, the constituent harmonic amplitudes F" are calculated individually, then combined to obtain the waveshape amplitude X,,(qR). The computations are carried out in accordance with the following discrete Fourier representation of a sampled periodic complex waveshape:

sin 5 nqR for q=l,2,3,... (Eq. 1)

wherein R is a frequency number which establishes the fundamental frequency of the generated note, n=l ,2,3 Wdesignates the harmonic or Fourier component being evaluated, and is a harmonic coefficient establishing the relative amplitude of the n'" harmonic. In a computor organ which implements equation I, each of the harmonic components F" has a frequency which is an integral multiple of the nominal fundamental frequency.

In accordance with one embodiment of the present invention (see FIG. 2) individual Fourier component amplitudes F'" are calculated according to the relationship:

pm (3 p /wn R-l for q= l,2,3, .(Eq. 2)

wherein n designates the order of the Fourier compo ncnt, v=nl designates the overtone being evaluated,

and r specifies the extend of frequency offset or anharmonically of the u'" overtone. The fundamental (n l) component usually is evaluated at the nominal fundamental frequency of the generated note. so that 1; =17,,=t). For each anharmonic overtone, the corresponding value of 1 will be non-Zero. Should 1 for a particular value of u. the corresponding 11 overtone will not be offset in frequency. but will be a true harmonic of the note being generated. The term nqR-I-ry herein is called the overtone sample point.

The Fourier component amplitudes F'" are summed to obtain the resultant wavcshape sample point ampli tude X,,(qR). That is:

IIMS

for q=l,2,3,... (Eq. 4)

In the computor organ, the waveshape amplitudes X,,(qRl generally are computed at regular time intervals 1,. At each successive time interval 1, the value qR is incremented in an adder of modulo N, where N is related to the number of sample points per period of the highest frequency note produced by the instrument. The fundamental amplitude F is evaluated at successive, equally separated sample points. However, for each anharmonic overtone. the distance between Sam ple points at which the amplitude of that overtone is evaluated is designated by (n-I-(n itself is changing periodically with time (i.e., is being incremented at intervals 1,, resetting at modulo N), the separation between overtone sample points. determina tive of the anharmonically of that overtone. also will change with time. That is. the extent of anharmonicity of each overtone will be periodic. Moreover. the periodicity of the anharmonicity will be smaller at the high frequency end of the scale (where the R values are greater) than at the low frequency end. It is this effect which facilitates. inter alia, octave decoupling in the computor organ.

In alternative embodiments of the invention, the overtone anharmonicity is independent of time. Thus, in the computor organ of FIG. 9, each overtone has a constant frequency offset which does not vary in time. and which is the same for all notes generated by the instrument. In this embodiment, the Fourier component amplitudes are calculated in accordance with the relationship:

)/qR) R. Since q g P" (1, sin (rr/ll') Inc/Rw I n Sin (YT/w) (nqR+vJr J for 11 12.3. (Fq. 5

wherein 1 vJq and J is a constant: preferably .1 z 2"" with k being an integer. A characteristic of such embodiment is that the extent of overtone offset is the same for all keys on the manual. Thus, the first overtone of each note may be displaced by say +2Hz from the nominal second harmonic frequency. regardless of what note is being played.

In the preferred forms of the invention shown in FIGS. [0 and 11 the overtone anharmonically does not vary in time, but is a function of the note being genen ated. In these embodiments, each overtone is offset by a constant number of cents, where a cent is 1/1200 of an octave. Each Fourier component amplitude is calculated by the equation: F C sin(rr/W)(nqR+n wherein n "=v(qR/K) and K is a constant. preferably K 1 with Z being an integer. Instruments using such constant cents overtone offset have a particularly pleasing sound over the entire range of the keyboard. BRIEF DESCRIPTION OF THE DRAWINGS A detailed description of the invention will be made with reference to the accompanying drawings wherein like numerals designate corresponding parts in the se\'- eral figures.

FIG. 1 is a typical harmonic spectrum of a musical note produced by a computor organ employing anharmonic overtone generation.

FIG. 2 is an electrical block diagram of a single channel computor organ including anharmonic overtone generation in accordance with equation 3 above.

FIGS. 3, 4 and 5 show alternative circuits for providing overtone offset (1 values; and useful in conjunction with the computor organ of FIG. 2.

FIG. 6 is an electrical block diagram showing implementation of anharmonic overtone generation in a parallel processing computor organ.

FIG. 7 is a typical harmonic spectrum of a musical note wherein odd and even overtones are offset in opposite frequency directions.

FIG. 8 shows alternative circuitry for providing overtone offset values to the parallel processing computor organ of FIG. 6.

FIG. 9 is an electrical block diagram of a computor organ wherein constant frequency offset, anharmonic overtone generation is implemented in accordance with equation 5 above.

FIGS. 10 and I] are electrical block diagrams of computor organ embodiments wherein anharmonic overtones having constant cents frequency offset are generated in accordance with equation 6 above.

FIG. 12 is an electrical block diagram of circuitry for modulating the anharmonic overtones as a function of time.

FIG. 13 is a harmonic spectrum of a typical note produced by a computor organ employing anharmonic overtone generation, wherein the fundamental frequency is detuned so that the subjective fundamental recreated from offset overtones will be in tune.

DESCRIPTION OF THE PREFERRED EMBODIMENTS The following detailed description is of the best presently contemplated modes of carrying out the invention. This description is not to be taken in a limiting sense. but is made merely for the purpose of illustrating the general principles of the invention since the scope ofthe invention best is defined by the appended claims.

Structural and operational characteristics attributed to forms of the invention first described also shall be attributed to forms later described. unless such characteristics obviously are inapplicable or unless specific exception is made.

FIG. 1 shows the harmonic spectrum of a typical musical note produced by a computor organ using anharmonic overtone generation in accordance with the present invention. The spectrum contains a fundamental ll evaluated at the nominal fundamental frequency f of the note, and anharmonic overtones ]2l5 having frequencies which are not integral multiples off. The first overtone 12 has a frequency Zf'l'l/ wherein u, designates the offset of this overtone with respect to the frequency 2f of the true second harmonic. Similarly, the typical non-harmonic overtones l3, l4 and are evaluated at respective frequencies 3f+u ift-v and loft-11, which are offset by the amounts v v and 1/ from the frequencies 31', 4f and 16f of the true third, fourth and sixteenth harmonics. (In FIG. I, the solid lines designate Fourier components actually generated by the computor organ; the dotted lines indicate the harmonics which are not generatedl Musical notes having non-harmonic overtones are produced by the computor organ 18 (FIG. 2) which implements anharmonic overtone generation in accordance with equation 3 above ln general, circuitry and operation of the computor organ 18 is as described in the US. patent application, Ser. No. 225,883. However. the computor organ 18 includes an overtone offset (1 memory 19, an v memory address control 20 and an adder 2] which implement frequency offsetting of selected Fourier components.

The computor organ 18 of FIG. 2 operates to produce via a sound system 21 a musical note selected by the keyboard switches 22. This is accomplished by cal culating the discrete Fourier components associated with amplitudes at successive sample points of a waveshape characterizing the selected note. The compo nents are algebraically summed in an accumulator 23 which. at the end of each computation time interval t, containsthe amplitude at the current sample point. This amplitude is provided via a gate 24, enabled by the I signal on a line 25, to a digital-to-analog converter 26 which supplies to the sound system 21 a voltage corresponding to the waveshape amplitude just computed. Computation ofthe amplitude at the next sample point subsequently is initiated. so that the analog voltage supplied from the converter 26 comprises a musical waveshape generated in real time.

The period of the computed waveshape. and hence the fundamental frequency of the generated note. is established by a frequency number R selected by the keyboard switches 22. A set of such frequency numbers corresponding to the notes of the instrument is stored in a frequency number memory 27. The tonal quality of the produced musical note is established by the set of harmonic coefficients 0,, stored in a memory 28 and used in computing the Fourier components at each sample point. In general. the use of lo Fourier components W=lhi is quite satisfactory for synthesizing mu sical instrument sounds.

The computor organ l8 implements equation 3 by computing the amplitude value X,,(qR) for each sample point during a time interval l The individual Fourier component amplitudes 1" (see equation 2) for each of the W=l 6 components are calculated separately during successive time intervals 1 through 1 established by a clock 31 and a counter 32. At the first interval the amplitude F" of the fundamental is calculated. This value F is placed in the accumulator 23. At the interval 1, the amplitude P of the second Fourier component (i.e. the first overtone) is computed and added to the accumulator 23 contents. At time r the second overtone amplitude F is calculated and added to the accumulator 23. The routine is terminated when all W Fourier components have been evaluated. Upon such termination. the algebraic sum contained in the accumulator 23 will correspond to the amplitude X,,(qR) for the sample point designated by the value qR.

As noted earlier, the waveshape amplitude X (qR) in the accumulator 23 is gated to the digital-to-analog converter 26 at the end of the computation interval 1,. The accumulator 23 then is cleared by the signal on the line 25, and computation of the amplitude at the next sample point subsequently is initiated. The value qR is incremented and the W harmonic component ampli tudes F' are calculated for the sample point designated by the new value of qR. Eventually the entire waveshape will be generated, the sound system 21 re producing the musical note as the amplitude computations are carried out.

ln the system of FIG. 2, a note interval adder 33 contains the value qR identifying the sample point at which the waveshape amplitude currently is being evaluated. This value qR is incremented at the beginning of each computation interval 1, by adding the selected freguency number R to the previous contents of the adder 33. The selected value R is supplied to the adder 33 via a gate 34 enabled by the I signal on the line 25. Preferably, the adder 33 is of modulo N where N is the prodact of the R number for any note times the number of points per period of that note.

To calculate each Fourier component, the values nqR (for n 1,2. W) are obtained in a harmonic interval adder 35 which is cleared before each amplitude computation cycle. Upon occurrence of the first t clock pulse of a new cycle, the current value qR contained in the note interval adder 33 is entered into the harmonic interval adder 35 via a line 36 and a gate 37. At each subsequent I", clock pulse. the value qR is added to the previous contents of the adder 35. As a re sult, the harmonic interval adder 35 will contain the value nqR for the n'" order Fourier component currently being evaluated. Preferably the harmonic inter' val adder 35 also is of modulo N.

To implement production of anharmonic overtones. the frequency offset value 1 of the v' overtone is added to the value nqR by the adder 2]. The value nqR is obtained from the harmonic interval adder 35 via a line 38. The output of the adder 21, provided on a line 41, thus represents the sum (nqR-l-n The frequency offset value 1 is supplied to the adder 20 from the overtone offset (1;) memory 19 via a line 42. The 1 memory 19 is accessed by the address control circuit 20 which receives the timing pulse !,.,,,-l,.,, via a line 43 from the counter 32. Thus. e.g., at the time during which the second (n=2) Fourier component (i.e.. the first overtone) is being calculated. the signal on the line 43 will cause the address control 20 to access the overtone offset value m from the memory [9.

The value sin (Tr/W) tnqR+17 corresponding to the argument (nqR+n received via the line 4] from the adder 20 is accessed from a sinusoid table 46 by an address decoder 47. The sinusoid table 46 may comprise a read only memory storing values of sin (IT/W d) for d: s 2W at intervals of D. where D is called the resolution constant of the memory.

The value sin YT/W (itqRlYJ supplied via a line 48. is multiplied by the coefficient C for the corresponding n' Fourier component by a multiplier 50. The multiplication product represents the amplitude F" of the 11" Fourier component and is supplied via the line 51 to the accumulator 23. The appropriate coefficient C is accessed from the harmonic coefficient memory 28 by an address control 35 which receives the calculation timing signals via the line 43.

In the embodiment of FIG. 2, arbitrary values ofn, may be stored in the memory 19. The values may be the same or different for each overtone. The value 17,, for a certain overtone may be zero in which case a true harmonic with no frequency offset will be evaluated.

The overtone offset (1 memory 19 and the associated address control 20 advantageously may be implemented using a single integrated circuit such as the Signetics type 8223 programmable read only memory. Full word decoding is included in this integrated circuit chip, which accepts a binary address input. A binary counter such as the Signetics integrated circuit type 8281 advantageously is used as the counter 32; the buss 43 may comprise the binary output lines from that counter. Any desired overtone offset (17) values can be user programmed into this integrated circuit memory. The adder 21 may comprise a Signetics type 8268 inte' grated circuit adder. Integrated circuitry useful for implementing the other components of the computor organ 18 are described in the related applications listed above. Similarly, typical values of R and C are tabulated in those related applications. The following Table A lists typical conventional integrated circuits that may be employed as certain of the components of the instrument shown in FIG. 2.

TABLE A Conventional intergrated circuit*(or other reference) Component (FIG. 2)

Frequency number memory 27 Note interval (a) adder 33 SIG. 8268 gated full adder [p.97]

Tl SN5483. SN7483 4-bit binary full adders [pH-271 I (may be connected as shown in Flores Section ll.l to accumulate sum Same as note interval adder 25.

Hannonic interval adder 35 Component Integrated Circuit Conventional intergrated circuitlor other reference] Component FIG. 2 l

(m tes 24.34.37 TI SN5408. SN5409 quadruple AND gates [p.(vl 7 (at Tl TMS44ll5 sinusoid tahle and addressing eir cultry Tl TMS44UU ROM containing 5l2 words of 8-bits [p.l4-l88] programmed to store sin values SIG 8277 sixteen bit shift registerlp. l 2] I; address control implemented by connecting t,. clock line 2] (FIGI l to the shift register input which controls shift.

Tl SN54I66 series shift registers |p.'-J-l 34| Also can he implimented using a read only memory such as SIG 8223 which includes address control circuitry May he implemented as shown in application sheet SIG catalog. p.28 using SIG B202 buffer registers and R260 arithmetic element Also can be implemented using Slg 8243 sealer [p.65]

SIG. 8268 or Tl SN5483. SN7483 full adders connected as shown in Flores. section I l.l "Aceumulators".

Sinusoid table 41 and memory address decoder 47 Harmonic coefficient memory 28 and memory address control 35 Harmonic Amplitude (all Multiplier 5U Accumulator 23 (a) TI Texas Instrument Co. (Page references are to the TI Integrated Cireuiits Catalog for Design Engineers." first Edition. January. l972| SIG Signetics. Sunmvalc. California llage references are to the SIG "Digitial 8001) Series TIIJMSI" catalog. copy right I97] I Flores. Iran Computer Logic" Prentice-Hall, l ihtl.

FIG. 3 shows a modified version of the computor organ 18 which also implements equation 3. In this embodiment, 1 =v1y for each overtone. Thus the first (v=l overtone has an offset established by a value of n stored in a register 53. The second (v=2) overtone is evaluated with an offset 21 and each higher order overtone has an offset 1m.

With this arrangement. the m, values need not be stored individually in a memory. but can be calculated during the waveshape amplitude computation cycle. Thus the overtone offset memory I8 and address control 19 shown in FIG. 2 are not used; rather the overtone offset values w; are provided via a line 42' to the adder 40 (FIG. 2) by the circuit of FIG. 3. The value in is accumulated in an adder 54 which is cleared at the end of each computation cycle by the 1, signal on the line 25. During the first calculation interval r when the fundamental is being evaluated. the contents of the adder 54 is zero so that no offset is introduced;

thus the ln=l component will be e\aluated at the true fundamental frequency of the note being generated.

To provide the overtone offset values in the value 1 stored in the register 53 is added repetitively to the previous contents of the adder 54 at successive overtone calculation times I,.,,. through r To this end. the value 1 is supplied to the adder 54 via agate S6 enabled by the corresponding timing signals on a line 43' from the counter 32. Occurrence of the timing signal 1, causes the value 1 to he transferred from the register 53 to the adder 54. Accordingly. the value 11 1 will he provided via the line 42' to the memory address do coder 47 of FIG. 2 during calculation of the first over tone. During successive calculation intervals r,.,, through r the value 1 will be added successively to the adder 54 contents. so that the required value my will be supplied to the eomputor organ I8.

The value of n stored in the register 53 (FIG. 3) is or bitrary. It may be constant for all notes of the scale; or it may differ for different notes. FIGS. 4 and 5 show circuits for providing to the register 53 values of 1 which are functions of the selected note. In the embodiment of FIG. 4. the note dependent overtone offset value '1) R/K is obtained by dividing the frequency number R by a constant k. This is implemented by a divider 59 which receives the R number via a line 27' from the frequency number memory 27 and which supplies the quotient r; R/K to the register 53 via a line 60. In this embodiment, the overtone offset will be a constant number of cents. but however the anharmonicity will vary periodically in time since the waveshape amplitude is computed in accordance with equation 3 above.

FIG. 5 shows a more generalized system for producing frequency proportional overtone anharmonicity.

The circuit incorporates a function element 61 which implements an arbitrary transfer function n=f(R). The circuit 6I receives the selected frequency number R from the memory 27 and provides via a line 60' to the register 53 (FIG. 3) the value 17=f(R). Note that the divider 59 (FIG. 4) is a specialized embodiment of the general circuitry of FIG. 5.

Anharmonic overtone generation in accordance with equation 3 likewise can be implemented in a parallel processing eomputor organ of the type disclosed in the US. patent application. Ser. No. 298.365. Such an implementation is shown in FIG. 6 wherein the eomputor organ 65 includes two parallel processing channels 66A. 66B. Half of the Fourier components utilized in the waveshape amplitude computation are calculated in one channel 66A. and the remaining components are evaluated concurrently in the other channel 668.

In the embodiment of FIG. 6, separate overtone offset (mmemorics I9A. I9B and related 17 memory address control circuits 20A. 20B are provided in the respective channels 66A. 668. In the channel 66A the values nqR for certain values of n are supplied via a line 38A during consecutive calculation time intervals I through I,.,,,. to an adder 21A. The appropriate overtone offset values 1;. are provided to the adder 21A from the memory IJA, so that the output of the adder 21A represents the quantities nqR+17,. for the set of Fourier components evaluated in the hannel 66A. This output. on a line 41A, is provided to the sinusoid table and address decoder 46A. which provides the values sin(nqR+n. These sin values are multiplied by the appropriate harmonic coefficients supplied from a memory 28A by a harmonic amplitude multiplier 50A to produce on a line 48A the Fourier component values F" I sin w/lluiqR-l-n, for those components evaluated in the channel 66A.

The remaining Fourier components are similarly evaluated in the parallel channel 668. wherein corresponding circuit blocks are identified by like numerals followed by the letter The Fourier components present concurrently on the lines 48A and 48B are summed in an adder 67 and provided to an accumulator. digital-to-analog converter and sound system (not shown) analogous to those shown in FIG. 2.

Different sets of Fourier components may be evaluated in the two processing channel 66A, 668. For example. the first eight (11 11.3. 8) low order Fourier components may be calculated in the channel 66A, and the high order (n=9.l0,l I, l6) Fourier components in the channel 668. In this case. the overtone offset memory 19A will contain the values 1 through 1;; which are accessed at the respective time intervals through I The overtone offset memory 19B will contain the values m through 17, which are accessed at the consecutive time intervals r,.,,, through I when the corresponding 8th through 15th overtones (i.e., the 9th through 16th Fourier components) are evaluated.

In another embodiment. the odd (n=l,3.5. l5) Fourier components may be evaluated in the channel 66A and the even (n=2,4,6 l6) Fourier components (corresponding to the odd overtones) may be calculated in the other channel 668. In that case. the overtone offset memory 19A will contain the values 17 .11 1 17 the overtone offset memory I9B will contain the values n n- 17;, 0.

It is not necessary that all overtones be frequency offset in the same sense. Some of the overtones may be offset sharp and others flat. This is illustrated by the harmonic spectrum of FIG. 7, wherein the odd overtones (even Fourier components) are offset sharp and the even overtones are offset flat. Production of such notes readily is implemented by the FIG. 9 eomputor organ embodiment described in the preceeding paragraph. Negative offset (1 values are stored in the memory 19A and positive 1 values are stored in the memory 198. With this arrangement. e.g., will be calculated using a positive value 7 to provide an anharmonic overtone 70 (FIG. 7) which offset is sharp. The second overtone 71, evaluated in the processing channel 668, will be flat.

A system analogous to that shown in FIG. 3 may be used to provide overtone offset values to the parallel processing eomputor organ of FIG. 6. Such an arrangement. shown in FIG. 8, is useful in the embodiment wherein the low order Fourier components are evaluated in one channel 66A and the high order components are evaluated in the other channel 668. The ap propriate 1/ values are supplied to the adders 21A, 218 (FIG. 6) from respective accumulating adder circuits 72A. 728 which are cleared at the end of each computation cycle; the overtone offset memories 19A, 19B are not used.

A pair of registers 73, 74 respectively store the values 1 and 81 During the first calculation interval I the contents of the adder 72A is zero. Accordingly. the fundamental (n=l Fourier component is evaluated in the channel 66A with no frequency offset (i.e. at the nominal fundamental frequency of the generated note) During each successive interval 1, through 1, the value 1; is gated to the adder 72A via a line 76 and added to the previous contents of that adder. Thus the adder 72A will contain the values 17,211,311, 71 at the corresponding times that the first through seventh overtones are evaluated in the channel 66A. These val ues w are supplied via the line 42A to the adder ZIA in the computor organ of FIG. 6. For channel 668. at time 1, the value 81; is gated from the register 74 via a gate 77 to the adder 728. Thus during the calculation interval I the overtone offset value 81 is susplied via the line 428 to the adder 218 in the computor organ 65; during this interval the eighth overtone is being evaluated in the channel 663. On successive calculation intervals 1 through r the value 1; is provided via the gate 75 and the line 76 to the adder 728 wherein the values 91 through 151; will be accumu lated. These are the appropriate offset values utilized by the channel 668 for evaluation of the high order overtones.

A different implementation of anharmonic overtone generation is employed in the computor organ 80 of FIG. 9. This embodiment provides constant frequency offset of the overtones, independent of time. in accordance with equation above. The computor organ 80 produces musical notes having a harmonic spectrum similar to that shown in FIG. I, but wherein the fundamental is evaluated at the true fundamental frequency f of the note being generated and each overtone l2, l3 has a frequency nf+ 111 where v n I.

In the computor organ 80 (FIG 9), the frequency number R of the selected note is gated to the note interval adder 33 at the beginning of each waveshape amplitude computation cycle. Thus the note interval adder 33 provides on the line 36 the value qR. At each component calculation interval r through r this value qR is supplied via a gate SI to a non'accumulating adder 82. During the initial interval I the second input to the adder 82 is zero, so that the value qR is supplied via the line 83 to the harmonic interval adder As a result, the first Fourier component is evaluated at the nominal fundamental frequency of the selected note. At each successive calculation interval 1, through t the value Jq is supplied to the adder 82 via a gate 84 and a line 85, so that the value (qR-l-Jq) is provided via the line 83 to the harmonic interval adder 35. As a result, the arguments (nqR+vJq) will be presented to the memory address decoder 47 via the line 41 during the consecutive Fourier component calculation intervals. The sin values corresponding to these arguments will be provided via the line 48' from the sinusoid table 46 to a harmonic interval multiplier 50, accumulator 23, digital-to-analog converter 26 and sound system 21 like that of FIG. 2. To obtain the values Jq, the constant J is stored in a register 87 (FIG. 9). Preferably, but not necessarily, the value J=2*" where k is an integer of l or greater. The value J is added to the previous contents of an accumulating adder 88 (of modulo N) upon occurrence of the computation cycle timing signal I, which enables a gate 89. The contents of the adder 88 thus represents the value Jq.

A computor organ 90 which implements equation 6 above is shown in FIG. 10. In this embodiment each an harmonic overtone is offset by an amount which is a constant number of cents. The anharmonicity is inde pendent of time.

To evaluate the fundamental without frequency offset, the value qR from the interval adder 33 is supplied to the harmonic interval adder 35" at the interval t via a gate 9] and a non-accuniulating adder 92 the other input of which is zero during this 1 interval. On each of the successive overtone calculation intervals 1 through 1 the value z Rfls'. where K is a constant. is added to the value qR in the adder 92 and the sum (qR-H qR/K)) is supplied via the line 93 to the harmonic interval adder 35". As a result. the arguments tnqR+v(qR/K)) are provided to the sinusoid table 46, exactly in accordance with equation 6 above.

The value qR/k is obtained by dividing the value qR from the line 36 by the constant K in a divider circuit 94. Preferably the constant K=2 where z is an integer of I or greater. In a digital system, the divider circuit 94 may comprise a shift register, since right shifting is the equivalent of dividing by a power of 2. The divided qR/k is provided to the adder 92 via a line 95 and agate 96 which is enabled by the calculation timing signals 1, through provided via a line 97 from the counter 32.

The computor organ of FIG. I] implements equation 6 above in an alternative manner. The frequency number R obtained on the line 27' is divided by the constant K in a divider circuit 100. At the beginning of each computation cycle, the dividend R/K is gated to an accumulating adder 101 of modulo N via a gate 102 enabled by the t signal on the line 25. Thus the output of the adder 101, present on a line 103, represents the quantity qR/K As in the embodiment of FIG. 10, the constant K preferably is given by K=2 where g is an integer of l or greater.

During the first calculation interval I when the fundamental is evaluated. only the value qR on the line 36 from the note interval adder 33 is supplied via the gate 9] and the non-accumulating adder 92' (FIG. 11) to the harmonic interval adder 35". Thus the (n=l Fourier component is evaluated at the nominal funda mental frequency of the generated note. During each successive calculation interval r through 1 the value q(R/K) from the adder 101 is supplied to the adder 92 via the gate 96' for addition to the value qR which also is gated to the adder 92'. The sum (qR+q(R/K)) is supplied on the line 93', resulting in evaluation of the desired constant cents offset anharmonic overtones.

The embodiments of FIG. 9, l0, and 11 are shown in single processing channel computor organs, similar arrangements can be implemented in parallel processing instruments. In such instance, separate harmonic interval adders would be provided in each processing channel. To such adders would be supplied the appropriate values qR+JQ or qR-l-q(R/K) for generation in each channel of selected subsets of the desired anharmonic overtones.

Particularly interesting effects are achieved by modulating the anharmonic overtones a function oftime. For example. the frequency offset values 17 themselves may be modulated at a low frequency, typically on the order of 6 Hz, to produce a vibrato-like effect. This can be implemented using the circuitry of FIG. 12 wherein the value 1; to be time modulated is supplied via a line [05 to an adder 106. The output of an oscillator I07 operating at the modulation frequency is converted to a digital signal by an analog-to-digital (A/D) converter I08 the digital output of which is summed with the value 1 by the adder 106. The output of the adder 106 on a line 109 comprises a time varying overtone offset value 17(1').

'l he circuit of FIG. 12 may be used in conjunction with the computor organ 18 of FIG. 2 by inserting the adder I06 (FIG. l2) in series with the line 42 (FIG. 2). That is. the line 42 would be opened. the 1 values from the overtone offset memory l9 would be provided to the line I05, and the time modulated \alues nlj') on the line 109 would be supplied to the adder 2].

Alternatively. the time modulation circuit of FIG. 12 may be used with the computor organ embodiments of FIGS. 9. 10 or ll. For example. the adder 106 (FIG. 12) may be inserted in the line 85 (or the line 88') of FIG. 9 to time modulate the overtone offset value Jq. Likewise. the circuit of FIG. [2 may be inserted in the line 95 of FIG. 10 or the line [03 of FIG. ll to time modulate the offset value qR/k in these embodiments.

A characteristic of human hearing is that the car hecomes less sensitive at low frequencies. Because of this roll off" of hearing ability. the first overtone ofa note having low fundamental frequency may appear to the listener to have a greater amplitude than the fundamental. In such instance. the listener may subjectively sense the fundamental at a frequency which is half that ofthe first overtone. Thus at the low frequency end of the keyboard range. a note having anharmonic overtones may seem sharp or flat because the listener is detecting the fundamental subjectively at half of the first overtone frequency. For example. referring to the harmonic spectrum of FIG. 1, the listener may sense a subjective fundamental at a frequency V2(2 f-l-'n )=f-l-n,/2 slightly sharp with respect to the actual fundamental frequency This effect can be overcome by selecting the values of R and r; for low frequency notes such that the subjective fundamental will coincide with the nominal fundamental frequency of the note. This is illustrated by the harmonic spectrum of FIG. 13. The frequency number R is selected so that the fundamental component H1 is evaluated by the computor organ at a fre quencyj which is flat with respect to the nominal fundamental frequencyfof the note being generated. The offset value m is selected so that the first overtone 112 will be produced at a frequency 2f=2f'+'n which is exactly twice the nominal fundamental frequencyf. As a result. because of reduced hearing ability at the low frequencies, the listener will hear a subjective funda mental H3 at half the frequency of the first overtone. i.e., at exactly the nominal frequencyfof the selected note. The actual fundamental component lll, although flat. will be sensed only slightly because of the hearing roll off. The note will seem to the listener to be in tune. and to have the desired anharmonic overtone quality.

Intending to claim all novel. useful and unobvious features shown or described. the inventor makes the following claims:

I. An electronic musical instrument for synthesizing musical tones having anharmonic overtones. comprising:

evaluation means for individually calculating the constituent Fourier component amplitudes F of a musical \\".l\t.5hll[)t. in accordance with the rela tionship P" sin lrr/llltnqR-l-n wherein R is a frequency number establishing the fun damental frequency of the note. n=l 2. 3. Wdesignatcs the Fourier component and v=nl designates the overtone being evaluated. (1, is a harmonic coefficient establishing the relative amplitude ofthe n" Fourier component. 1 specifies the evtent of anharmonicity of the 11" overtone. and q is an integer incremented at regular time intervals I,. all W ofsaid constituent Fourier components being evaluated within each of said intervals 1,.

accumulator means for combining said separately calculated Fourier component amplitudes to obtain during successive time intervals I, the waveshape sample point amplitudes for successive sample points qR, and

converter means for converting said sample point amplitudes to musical tones as said calculations are carried out.

2. An electronic musical instrument according to claim 1 further comprising overtone offset means for providing to said evaluation means a selected value 1 =11? for each evaluated overtone. wherein 'r is a constant.

3. An electronic musical instrument according to claim 2 further comprising overtone offset means for providing to said evaluation means a selected value 17,, =v-q=vJq for each evaluated overtone, wherein J is a constant. the overtones of each synthesized tone thereby being offset by a constant frequency.

4. An electronic musical instrument according to claim 1 further comprising overtone offset means for providing to said evaluation means a selected value. 1; =1 (qR/k) for each evaluated overtone, K is a constant. the overtones of each synthesized tone thereby being offset from integral multiples of the note fundamental frequency by a constant number of cents.

5. An electronic musical instrument according to claim 1, wherein said evaluation means comprises:

a memory storing said harmonic coefficients C a sinusoid table comprising a storage device containing a set of sinusoid values at regular angular intervlas.

note selection switches for selecting a value R,

overtone offset means for providing a selected value 1; for each evaluated overtone, and

Fourier component evaluation circuitry utilizing said memory and said sinusoid table to evaluate F"' =C,,sin(1r/ W)(nqR+-q )for each oft/1e W constituent Fourier components in accordance with the selected value R and the provided values y.

6. An electronic musical instrument according to claim 5, wherein said Fourier component evaluation circuitry comprises:

a note interval adder for adding said selected value R to the previous contents of said note interval adder at the beginning of each time interval 1,, the contents of said note interval adder thereby representing qR.

argument combining circuitry for combining the values qR obtained from said note interval adder and the values 1 provided from said overtone offset means to obtain the arguments nqR-Pn for each order n=l, 2. 3, W. Fourier component.

sin evaluation circuitry. receiving said arguments rigR-H from said argument combining circuitry. for obtaining from said sinusoid table the value sint 1r/W)(nqR='n,, for each received argument nqR=n, and

a harmonic amplitude multiplier for multiplying each such sin value by the coefficient for the corresponding n'" harmonic component. the products of such multiplication being supplied to said accumulator means.

7. A musical instrument according to claim 6 wherein said overtone offset means comprises;

an overtone offset memory storing said values 1 a memory address control for accessing from said overtone offset memory the value 17,, corresponding to the n" Fourier component being calculated. and wherein said argument combining circuitry omprises;

a harmonic interval adder. cleared at the beginning of each time interval r,. for repetitively adding the value qR obtained from said note interval adder to the previous contents of said harmonic interval adder. the contents of said harmonic interval adder thereby representing ngR where n equals the number of such repetitive additions since the beginning of each time interval 1;. and

an adder for summing each value ngR obtained from said harmonic interval adder with the corresponding value 1;, accessed from said overtone offset memory. the resultant sum ngR-Pq being provided to said sin evaluation circuitry.

8. An electronic musical instrument according to claim 6, wherein said argument combining circuitry comprises;

a harmonic interval adder. cleared at the beginning of each time interval 1,.

an accumulating adder incremented by a constant amount J each time interval r,. the contents of said accumulating adder representing the quantity Jq. and

adder means for providing the value qR from said note interval adder to said harmonic interval adder during calculation of the (n=l l'" Fourier component and for providing the value qR=Jq to said harmonic interval adder during calculation of each other Fourier component. the accumulated contents of said harmonic interval adder thus representing the argument nqR+vJq.

9. An electronic musical instrument according to claim 6. wherein said argument combining circuitry comprises;

a harmonic interval adder. cleared at the beginning of each time interval r,.

a divider for dividing the value qR obtained from said note interval adder by a constant K. the output of said divider representing the value qR/k. and

adder means for providing to said harmonic interval adder the value qR from said note interval adder during calculation of the ("=1 Fourier component and for providing the value qR-t-qR/K to said harmonic interval adder during calculation of each other Fourier component. the accumulated contents of said harmonic interval adder thus representing the argument nqR-t-vtqR/K).

10. An electronic musical instrument according to claim 6, wherein said argument combining circuitry comprises;

a harmonic interval adder cleared at the beginning of each time interval 1,.

l 6 a divider for dividing the selected value R by a con stant K to provide the quotient R/K. an accumulating adder. the value R/K being added to the previous contents of said adder at the beginning of each time interval l so that the contents of said adder represents the quantity qR/K. and adder means for providing to said harmonic interval adder the value qR from said note interval adder during calculation of the (n=l Fourier component and for providing the value qR+qR/K to said harmonic interval adder during calculation of each other Fourier component. the accumulated contents of said harmonic interval adder thus representing the argument nqR-l-v(qR/K). 11. In an electronic musical instrument of the type wherein musical notes are generated by computing the amplitudes of a musical waveshape at successive sample points at certain regular time intervals from stored harmonic coefficient values. each amplitude being computed by individually calculating a set of constituent Fourier components of said waveshape. each Fourier component being calculated by multiplying a trigonometric function of the Fourier component sample point by a harmonic coefficient value which establishes the relative amplitude of that component. and wherein these amplitudes are converted to musical notes as the computations are carried out in real time. the improvement wherein at least some of said Fourier components are overtones that are evaluated at frequencies offset from multiples of the fundamental frequency of said generated note so that said instrument will produce a synthesized waveshape containing anharmonic overtones. said instrument comprising:

first means for establishing at said regular time intervals the successive fundamental sample points qR at which the fundamental component is evaluated. where R is a constant frequency number establishing the fundamental frequency of the generated note and q is an integer incremented as each waveshape amplitude computation is completed.

second means for establishing, as each overtone is evaluated. an overtone sample point nqR-l-n, where n designates the order of the Fourier com ponent being calculated. u==nl identifies the corresponding overtone and n, designates the extent of frequency offset of the v overtone. and

means for utilizing the sample point qR established by said first means during calculation of teh fundamental (n=l Fourier component and for utilizing the overtone sample points nqR+11 established by said second means during calculation of the individual Fourier components of order n=2 and greater.

12. An electronic musical instrument of the type wherein musical notes are generated by computing the amplitudes of a musical waveshape at successive sample points and converting these amplitudes to musical notes as the computations are carried out in real time and wherein a plurality of generalized Fourier components are calculated separately and combined to obtain each waveshape amplitude. at least some of said Fourier components being overtones that are evaluated at frequencies offset from multiples of the fundamental frequency of said generated note to produce a synthe sized waveshape containing anharmonic overtones. the fundamental component being evaluated at successive sample points qR. where R is a constant frequency number establishing the fundamental frequency of the generated note and g is an integer incremented as each waveshape amplitude computation is completed, and wherein each overtone is evaluated at an overtone sample point nqR+'n,, where n designates the order of the Fourier component being calculated, v=nl identifies the corresponding overtone and m, designates the extent of frequency offset of the 1 overtone, said instrument comprising:

a note interval adder to which the value R is added at regular waveshape amplitude computation time intervals 1,, the contents of said note interval adder thereby specifying the fundamental sample point qR.

overtone offset means for providing the overtone offset value 17, during calculation of the corresponding (n=v+l Fourier component,

overtone sample point means, including a harmonic interval adder cleared before each computation cycle, and cooperating with said note interval adder and said overtone offset means, for establishing the overtone sample point nqR-Pn at which each overtone is evaluated,

a trigonometric function table comprising a memory storing values of a trigonometric function at regular angular intervals, and means for obtaining from said table a trigonometric function the argument of which corresponds to said overtone sample point nqR+n a harmonic amplitude multiplier for multiplying said trigonometric function by a coefficient C,, establishing the relative amplitude of the n'" Fourier component, and

an accumulator, cleared at the beginning of each computation cycle, for accumulating said scaled trigonometric functions, the contents of said accumulator at the completion of each computation cycle thereby representing said waveshape amplitude.

13. An electronic musical instrument according to claim 12 wherein said overtone offset means includes circuitry which provides values 17,, =1 (qR/K) where K is a constant, so that each overtone is offset by an extent which is proportional to the fundamental frequency of the note being generated.

14. An electronic musical instrument according to claim 12 wherein said overtone offset means includes circuitry which provides values 1;, =1; where v is a constant.

15. An electronic musical instrument according to claim 12 wherein said overtone offset means includes circuitry which provides offset values 1 =vJq where J is a constant, so that said overtones are offset by constant frequency amounts independent of the note being generated and independent of time.

16. An electronic musical instrument according to claim 12 including:

means for evaluating the (n=l Fourier component at a frequencyf different from the nominal fundamental frequency fof the note being generated and for evaluating the (11 1 overtone at a frequency f 71 f- 17. An electronic musical instrument according to claim 12 further comprising;

means for time modulating at least some of the offset values 1;, to produce time variant anharmonic overtones.

18. Apparatus for synthesizing musical sounds by computing in real time the amplitudes at successive sample points of a waveshape having anharmonic Fourier components, comprising:

means for designating the successive sample points qR at which said waveshape is sampled, the number R establishing the fundamental frequency of said waveshape, the value q being an integer incremented at regular amplitude computation intervals means for providing certain offset values 1 establishing the extent of anharmonicity of the corresponding Fourier components,

means, responsive to the designated sample point qR and to the provided values 17,, for obtaining each constituent Fourier component a trigonometric function value corresponding to an argument nqR+n where n designates the order of the Fourier component being evaluated and v=nl,

means for scaling each obtained trigonometric function by a coefficient C,, to establish the relative amplitude of the corresponding n" Fourier component, and

means for accumulating the scaled trigonometric function values during each computation cycle to establish the waveshape sample point amplitude, and further comprising:

converter and sound system means for converting the waveshape amplitudes established in said accumulating means to musical notes as the amplitude computations are carried out, and

note selection switches for selecting the number R which establishes the waveshape fundamental frequency and hence determines the musical note being generated, said apparatus implementing the equation lqR) C sin (nqRt-n included in each amplitude computation. 

1. An electronic musical instrument for synthesizing musical tones having anharmonic overtones, comprising: evaluation means for individually calculating the constituent Fourier component amplitudes F(n) of a musical waveshape in accordance with the relationship F(n) Cn sin ( pi /W)(nqR+ Eta ) wherein R is a frequency number establishing the fundamental frequency of the note, n 1, 2, 3, . . . , W designates the Fourier component and Nu n-1 designates the overtone being evaluated, Cn is a harmonic coefficient establishing the relative amplitude of the nth Fourier component, Eta specifies the extent of anharmonicity of the Nu th overtone, and q is an integer incremented at regular time intervals tx, all W of said constituent Fourier components being evaluated within each of said intervals tx, accumulator means for combining said separately calculated Fourier component amplitudes to obtain during successive time intervals tx the waveshape sample point amplitudes
 2. An electronic musical instrument according to claim 1 further comprising overtone offset means for providing to said evaluation means a selected value eta Nu eta for each evaluated overtone, wherein eta is a constant.
 3. An electronic musical instrument according to claim 2 further comprising overtone offset means for providing to said evaluation means a selected value eta Nu eta Nu Jq for each evaluated overtone, wherein J is a constant, the overtones of each synthesized tone thereby being offset by a constant frequency.
 4. An electronic musical instrument according to claim 1 further comprising overtone offset means for providing to said evaluation means a selected value, eta Nu (qR/k) for each evaluated overtone, K is a constant, the overtones of each synthesized tone thereby being offset from integral multiples of the note fundamental frequency by a constant number of cents.
 5. An electronic musical instrument according to claim 1, wherein said evaluation means comprises: a memory storing said harmonic coefficients Cn, a sinusoid table comprising a storage device containing a set of sinusoid values at regular angular intervlas, note selection switches for selecting a value R, overtone offset means for providing a selected value eta for each evaluated overtone, and Fourier component evaluation circuitry utilizing said memory and said sinusoid table to evaluate F(n) Cnsin( pi /W)(nqR+ eta ) for each of the W constituent Fourier components in accordance with the selected value R and the provided values .
 6. An electronic musical instrument according to claim 5, wherein said Fourier component evaluation circuitry comprises: a Note interval adder for adding said selected value R to the previous contents of said note interval adder at the beginning of each time interval tx, the contents of said note interval adder thereby representing qR, argument combining circuitry for combining the values qR obtained from said note interval adder and the values eta provided from said overtone offset means to obtain the arguments nqR+ eta for each order n 1, 2, 3, . . . W, Fourier component, sin evaluation circuitry, receiving said arguments ngR+ eta from said argument combining circuitry, for obtaining from said sinusoid table the value sin( pi /W)(nqR eta for each received argument nqR eta and a harmonic amplitude multiplier for multiplying each such sin value by the coefficient Cn for the corresponding nth harmonic component, the products of such multiplication being supplied to said accumulator means.
 7. A musical instrument according to claim 6 wherein said overtone offset means comprises; an overtone offset memory storing said values eta , a memory address control for accessing from said overtone offset memory the value eta corresponding to the nth Fourier component being calculated, and wherein said argument combining circuitry omprises; a harmonic interval adder, cleared at the beginning of each time interval tx, for repetitively adding the value qR obtained from said note interval adder to the previous contents of said harmonic interval adder, the contents of said harmonic interval adder thereby representing ngR where n equals the number of such repetitive additions since the beginning of each time interval tx, and an adder for summing each value ngR obtained from said harmonic interval adder with the corresponding value eta accessed from said overtone offset memory, the resultant sum ngR+ eta being provided to said sin evaluation circuitry.
 8. An electronic musical instrument according to claim 6, wherein said argument combining circuitry comprises; a harmonic interval adder, cleared at the beginning of each time interval tx, an accumulating adder incremented by a constant amount J each time interval tx, the contents of said accumulating adder representing the quantity Jq, and adder means for providing the value qR from said note interval adder to said harmonic interval adder during calculation of the (n 1)th Fourier component and for providing the value qR Jq to said harmonic interval adder during calculation of each other Fourier component, the accumulated contents of said harmonic interval adder thus representing the argument nqR+ Nu Jq.
 9. An electronic musical instrument according to claim 6, wherein said argument combining circuitry comprises; a harmonic interval adder, cleared at the beginning of each time interval tx, a divider for dividing the value qR obtained from said note interval adder by a constant K, the output of said divider representing the value qR/k, and adder means for providing to said harmonic interval adder the value qR from said note interval adder during calculation of the (n 1)th Fourier component and for providing the value qR+qR/K to said harmonic interval adder during calculation of each other Fourier component, the accumulated contents of said harmonic interval adder thus representing the argument nqR+ Nu (qR/K).
 10. An electronic musical instrument according to claim 6, wherein said argument combining circuitry comprises; a harmonic interval adder cleared at the beginning of each time interval tx, a divider for dividing the selected value R by a constant K to provide the quotient R/K, an accumulating adder, the value R/K being added to the previous contents of said adder at the beginning of each time interval tx so that the contents of said adder represents the quantity qR/K, and adder means for providing to said harmonic interval adder the value qR from said note interval adder during calculation of the (n 1)th Fourier component and for providing the value qR+qR/K to said harmonic interval adder during calculation of each other Fourier component, the accumulated contents of said harmonic interval adder thus representing the argument nqR+ Nu (qR/K).
 11. In an electronic musical instrument of the type wherein musical notes are generated by computing the amplitudes of a musical waveshape at successive sample points at certain regular time intervals from stored harmonic coefficient values, each amplitude being computed by individually calculating a set of constituent Fourier components of said waveshape, each Fourier component being calculated by multiplying a trigonometric function of the Fourier component sample point by a harmonic coefficient value which establishes the relative amplitude of that component, and wherein these amplitudes are converted to musical notes as the computations are carried out in real time, the improvement wherein at least some of said Fourier components are overtones that are evaluated at frequencies offset from multiples of the fundamental frequency of said generated note so that said instrument will produce a synthesized waveshape containing anharmonic overtones, said instrument comprising: first means for establishing at said regular time intervals the successive fundamental sample points qR at which the fundamental component is evaluated, where R is a constant frequency number establishing the fundamental frequency of the generated note and q is an integer incremented as each waveshape amplitude computation is completed, second means for establishing, as each overtone is evaluated, an overtone sample point nqR+ eta where n designates the order of the Fourier component being calculated, Nu n-1 identifies the corresponding overtone and eta designates the extent of frequency offset of the Nu th overtone, and means for utilizing the sample point qR established by said first means during calculation of teh fundamental (n 1) Fourier component and for utilizing the overtone sample points nqR+ eta established by said second means during calculation of the individual Fourier components of order n 2 and greater.
 12. An electronic musical instrument of the type wherein musical notes are generated by computing the amplitudes of a musical waveshape at successive sample points and converting these amplitudes to musical notes as the computations are carried out in real time, and wherein a plurality of generalized Fourier components are calculated separately and combined to obtain each waveshape amplitude, at least some of said Fourier components being overtones that are evaluated at frequencies offset from multiples of the fundamental frequency of said generated note to produce a synthesized waveshape containing anharmonic overtones, the fundamental component being evaluated at successive sample points qR, where R is a constant frequency number establishing the fundamental frequency of the generated note and g is an integer incremented as each waveshape amplitude computation is completed, and wherein each overtone is evaluated at an overtone sample point nqR+ eta where n designates the order of the Fourier component being calculated, Nu n-1 identifies the corresponding overtone and eta designates the extent of frequency offset of the Nu th oveRtone, said instrument comprising: a note interval adder to which the value R is added at regular waveshape amplitude computation time intervals tx, the contents of said note interval adder thereby specifying the fundamental sample point qR, overtone offset means for providing the overtone offset value eta during calculation of the corresponding (n Nu +1)th Fourier component, overtone sample point means, including a harmonic interval adder cleared before each computation cycle, and cooperating with said note interval adder and said overtone offset means, for establishing the overtone sample point nqR+ eta at which each overtone is evaluated, a trigonometric function table comprising a memory storing values of a trigonometric function at regular angular intervals, and means for obtaining from said table a trigonometric function the argument of which corresponds to said overtone sample point nqR+ eta , a harmonic amplitude multiplier for multiplying said trigonometric function by a coefficient Cn establishing the relative amplitude of the nth Fourier component, and an accumulator, cleared at the beginning of each computation cycle, for accumulating said scaled trigonometric functions, the contents of said accumulator at the completion of each computation cycle thereby representing said waveshape amplitude.
 13. An electronic musical instrument according to claim 12 wherein said overtone offset means includes circuitry which provides values eta Nu (qR/K) where K is a constant, so that each overtone is offset by an extent which is proportional to the fundamental frequency of the note being generated.
 14. An electronic musical instrument according to claim 12 wherein said overtone offset means includes circuitry which provides values eta Nu eta where Nu is a constant.
 15. An electronic musical instrument according to claim 12 wherein said overtone offset means includes circuitry which provides offset values eta Nu Jq where J is a constant, so that said overtones are offset by constant frequency amounts independent of the note being generated and independent of time.
 16. An electronic musical instrument according to claim 12 including: means for evaluating the (n 1)th Fourier component at a frequency f'' different from the nominal fundamental frequency f of the note being generated and for evaluating the ( Nu 1)th overtone at a frequency 2f''+ eta 1 2f.
 17. An electronic musical instrument according to claim 12 further comprising; means for time modulating at least some of the offset values eta to produce time variant anharmonic overtones.
 18. Apparatus for synthesizing musical sounds by computing in real time the amplitudes at successive sample points of a waveshape having anharmonic Fourier components, comprising: means for designating the successive sample points qR at which said waveshape is sampled, the number R establishing the fundamental frequency of said waveshape, the value q being an integer incremented at regular amplitude computation intervals tx, means for providing certain offset values eta establishing the extent of anharmonicity of the corresponding Fourier components, means, responsive to the designated sample point qR and to the provided values eta , for obtaining each constituent Fourier component a trigonometric function value corresponding to an argument nqR+ eta , where n designates the order of the Fourier component being evaluated and Nu n-1, means for scaling each obtained trigonometric function by a coefficient Cn to establish the relative amplitude of the corresponding nth Fourier component, and means for accumulating the scaled trigonometric function values during each computation cycle to establish the waveshape sample point amplitude, and further comprising: converter and sound system means for converting the waveshape amplitudes established in said accumulating means to musical notes as the amplitude computations are carried out, and note selection switches for selecting the number R which establishes the waveshape fundamental frequency and hence determines the musical note being generated, said apparatus implementing the equation 